Exotic Hill problem: Hall motions and symmetries

Our previous study of a system of bodies assumed to move along almost-circular orbits around a central mass, approximately described by Hill's equations, is extended to exotic (alias noncommutative) particles. For a certain critical value of the angular velocity, the only allowed motions follow the Hall law. Translations and generalized boosts span two independent Heisenberg algebras with different central parameters. In the critical case, the symmetry reduces to a single Heisenberg algebra.